Question

Joachim has 2/3 as many marbles as Leanne. Leanne has 1/2 as many marbles as Alex. If Alex has 36 more than Joachim, how many marbles do they have altogether?

Answer 1

Answer:

99 marbles

Step-by-step explanation:

Let number of marbles with Alex be $x$

Leanne has 1/2 as many marbles as Alex.

So,

Number of marbles with Leanne = $\frac{x}{2}$

Number of marbles with Joachim = $\frac{2}{3}(\frac{x}{2})=\frac{x}{3}$

Also, Alex has 36 more marbles than Joachim.

So,

Number of marbles with Alex = 36 + Number of marbles with Joachim

= $36+\frac{x}{3}$

So,

$x=36+\frac{x}{3}\\\\x-\frac{x}{3}=36\\\\\frac{2x}{3}=36\\\\\x=36(\frac{3}{2})\\\\x=54$

So,

Number of marbles with Alex = 54

Number of marbles with Leanne = $\frac{x}{2}=\frac{54}{2}=27$

Number of marbles with Joachim = $\frac{x}{3}=\frac{54}{3}=18$

Total number of marbles = $54+27+18=99$